#!/usr/bin/env python3 # これはちゃんと AC のはず from fractions import Fraction def make_convex_slope(A: list[int], B: list[int]) -> list[tuple[int, int]]: x, y = 0, 0 ret: list[tuple[int, int]] = [(0, 0)] seq = sorted([(Fraction(b, a), a, b) for a, b in zip(A, B)]) for _, a, b in seq: x += a y += b ret.append((x, y)) return ret def trajectory_solve( A: list[int], B: list[int], C: list[int], D: list[int] ) -> tuple[bool, list[tuple[Fraction, Fraction]]]: assert len(A) == len(B) == len(C) == len(D) assert sum(A) == sum(C) assert sum(B) == sum(D) assert min(A + B + C + D) >= 1 assert max(A + B + C + D) <= 100000000000000000 lo_polyline = make_convex_slope(A, B) hi_polyline = make_convex_slope(C, D) for (x0, y0), (x1, y1) in zip(lo_polyline, lo_polyline[1:]): for x, y in hi_polyline: if (x1 - x0) * (y - y0) - (y1 - y0) * (x - x0) < 0: return False, [] assert lo_polyline[0] == hi_polyline[0] == (0, 0) assert lo_polyline[-1] == hi_polyline[-1] == (sum(A), sum(B)) nx, ny = Fraction(0), Fraction(0) trajectory: list[tuple[Fraction, Fraction]] = [(nx, ny)] while (nx, ny) != lo_polyline[-1]: s = Fraction(1 << 60) # slope for px, py in hi_polyline: if px <= nx: continue s = min(s, Fraction(py - ny, px - nx)) assert s < Fraction(1 << 60) next_x = Fraction(sum(A)) for (px, py), (qx, qy) in zip(lo_polyline, lo_polyline[1:]): s2 = Fraction(qy - py, qx - px) if s2 <= s: continue # y = s * (x - nx) + ny と y = s2 * (x - px) + py の交点 # sx - s nx + ny == s2 x - s2 px + py # (s - s2) x == s nx - ny - s2 px + py next_x = min(next_x, (s * nx - ny - s2 * px + py) / (s - s2)) ny += s * (next_x - nx) nx = next_x trajectory.append((nx, ny)) ans: bool = False if len(trajectory) - 1 < len(A): ans = True else: abidx = sorted([(Fraction(B[i], A[i]), i) for i in range(len(A))]) cdidx = sorted([(Fraction(D[i], C[i]), i) for i in range(len(B))]) if [i for _, i in abidx] == [i for _, i in cdidx]: ans = True return ans, trajectory if __name__ == "__main__": input() A = list(map(int, input().split())) B = list(map(int, input().split())) C = list(map(int, input().split())) D = list(map(int, input().split())) ret, trajectory = trajectory_solve(A=A, B=B, C=C, D=D) print("Yes" if ret else "No")